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In proposing a major overhaul of the U.S. tax system, Republican presidential front-runner Donald Trump vows to reduce the tax rates paid by millions of Americans, spur economic growth not seen in decades and do so without adding to the national debt.

"It's a tax reform that I think will make America strong and great again," Trump said Monday. Here is a look at some of the claims Trump made when announcing his tax plan and how they compare with the facts.

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TRUMP: "It will provide major tax relief for middle income, and for most other Americans, there will be a major reduction."

THE FACTS: Trump's plan will undoubtedly reduce the amount of money Americans pay in income taxes. Kyle Pomerleau, an economist at the Tax Foundation, which advocates for lower tax rates, said the cost of Trump's cuts could easily total more than $7 trillion over the next decade.

For single people making less than $25,000, and married couples earning less than $50,000 a year, Trump would get rid of federal income taxes entirely. He also keeps the Earned Income Tax Credit, a benefit for low-income Americans they can claim even if they pay no taxes under the current system.

Trump would reduce the number of tax brackets from the current seven to four: 0 percent, 10 percent, 20 percent and 25 percent. While such a change would reduce taxes for middle-income earners, the "most other Americans" who would benefit the most would be those who make enough to fall into the current top tax bracket and pay 39.6 percent on income above $413,000.

Steve Gill, a tax and accounting professor at San Diego State University, said that as a group, Americans who are making more than $200,000 a year would pay $400 billion to $500 billion less in taxes annually under Trump's plan than under the current system.

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TRUMP: "It reduces or eliminates most of the deductions and loopholes available to special interests and to the very rich. In other words, it's going to cost me a fortune."

THE FACTS: Only Trump and his accountant can be sure, since he does not specify in his proposal exactly which deductions and loopholes he plans to eliminate and has yet to release any of his tax returns.

But it appears likely that Trump's plan would be a financial boon for someone of his wealth. Trump and his wife would pay 25 percent, instead of the current 39.6 percent, on any income above $300,001. An income statement he released alongside his personal financial disclosure report this past summer reported his 2014 income as $362 million.

His proposal to eliminate the 40 percent tax on inheritances of more than $5.4 million would allow him to pass on his estate to heirs tax-free, a savings worth billions given his estimated net worth of more than $10 billion.

And by cutting 10 percentage points from the current corporate tax rate of 35 percent, the Trump Organization and its hundreds of subsidiaries would pay less — assuming they don't already use tax strategies to reduce their effective rate below 15 percent.

THE FACTS: In order for Trump's tax rate reductions to be what's known in Washington parlance as "revenue neutral," he would have to offset them in some way. Several tax experts, even those who like Trump's reduction in rates, said his plan appears unable to do so.

Trump proposes making up some of that lost revenue by eliminating some deductions, but he's ruled out getting rid of those for home mortgage interest and charitable gifts, which are worth more than $120 billion a year.

Martin Sullivan, chief economist at a nonprofit tax analysis group and a former employee of the Congressional Joint Committee on Taxation, said adopting Trump's plan without increasing the deficit "doesn't look possible if you take the mortgage interest and charitable off the table."

To get anywhere near breaking even, Sullivan said, Trump would have to eliminate deductions for state and local taxes and perhaps begin taxing retirement savings in pensions and 401(k)s.

Many advocates of tax cuts argue they pay for themselves by boosting economic growth. But Ryan Ellis of Americans for Tax Reform, a low-tax advocacy group that Trump consulted as he developed his proposal, said Trump's cuts are so large that won't happen even under the most optimistic scenarios for growth. "It just doesn't square up," he said.

TRUMP: "We are reducing taxes, but at the same time if I win, if I become president, we will be able to cut so much money and have a better country. We won't be losing anything other than we will be balancing budgets and getting them where they should be."

THE FACTS: Even if Trump's tax plan winds up being revenue neutral, it wouldn't bring in enough money to balance the budget.

At the upcoming end of the current fiscal year, the Congressional Budget Office projects the deficit will end up at $426 billion. That means Trump would have to find that much spending to cut to balance the nation's books.

Trump pledged Monday to start by going after waste, citing the example of "hammers that cost $800 that you can buy in a store for a tiny amount of money" — a reference that dates to a defense program in the 1980s. He also poked fun at a government-funded soccer field that cost $1 million.

To make up the deficit, Trump would have to find 530 million such hammers or 426,000 soccer fields to cut from the budget.

Put another way, Trump would need to eliminate all improper or insufficiently documented payments made by the federal government — estimated by the Government Accountability Office at $124 billion in 2014 — more than three times over.